A vehicle equipped with an automatic transmission includes a forward/reverse switching mechanism (friction element) capable of switching engaged and released states according to a hydraulic pressure between an engine and the transmission, and the friction element is engaged when a driving range such as a D-range or an R-range is selected while being released when a non-driving range such as an N-range or a P-range is selected. The engaged and released states of the friction element is controlled by a line pressure which is a hydraulic pressure supplied from an oil pump driven by the engine. Since the oil pump also stops when the engine stops, the line pressure is reduced to release the friction element.
It is known to, in such a vehicle, automatically stop the engine when a predetermined automatic stop condition holds during a stopped state and restart the engine when a restart condition holds. Further, JP2000-153726A discloses that an engine is restarted and an instruction pressure to the friction element is suddenly increased to promptly engage a friction element when an engine restart condition holds.